Freefall - calculating g¶
Equation for calculating acceleration due to gravity is:
where \(g\) is the acceleration due to gravity, \(v1\) is the velocity in gate 1, \(v2\) is the velocity in gate 2 and \(\Delta t\) is the time between gates.
1) Setting up the photogates¶
On a single support stand [1], place the two photogates a distance apart. Make sure that the top (first) photogate is connected to the Photogate 1 position on the Arduino Shield.
![_images/photogates_3.png](_images/photogates_3.png)
2) Software¶
Set-up the software as described in the previous section Using the photogate software.
3) Sample data¶
In the example shown below, we used a 0.5” wide metal block (12.7mm). Hold the object slightly above the first photogate and release to drop it between the two gates. Save data for analysis.
![_images/wbd_drop.png](_images/wbd_drop.png)
4) Data analysis¶
From time in gates, calculate velocity, \(v\), of falling object:
- \(v\) = object length (m) / time in gate (s)
- \(v1\) = 0.0127/0.00940 = 1.351 \(\mathrm{m}/\mathrm{s}\)
- \(v2\) = 0.0127/0.00406 = 3.128 \(\mathrm{m}/\mathrm{s}\)
From equation, g is given by:
Footnotes
[1] | Additional equipment from Carolina Biologicals. Support Stand $15.50, Part # 707146 and Clamp Holder, $9.90, Part # 707310 |